一个新三维类洛伦兹系统的最终有界集和正向不变集及其在同步中的应用

J4 ›› 2010, Vol. 45 ›› Issue (9): 83-89.

一个新三维类洛伦兹系统的最终有界集和正向不变集及其在同步中的应用

杨洪亮1,张付臣2*,舒永录2,李云超3

1. 临沂师范学院信息学院, 山东临沂 276005; 2. 重庆大学数理学院, 重庆 400044;
3. 西北大学数学系, 陕西西安710127

收稿日期:2009-11-03 出版日期:2010-09-16 发布日期:2010-10-12
通讯作者: 张付臣(1983-),男,硕士,研究方向为混沌系统.
作者简介:杨洪亮(1974-),男,硕士,副教授,研究方向为计算机应用.Email:yanghongliang@lytu.edu.cn
基金资助:
国家自然青年科学基金资助项目(10601071);重庆市自然科学基金资助项目(2009BB3185)

The ultimate bound and positively invariant set of a new Lorenz-like chaotic system and its application in chaos synchronization

YANG Hong-liang1, ZHANG Fu-chen2*, SHU Yong-lu2, LI Yun-chao3

1. College of Information Science, Linyi Normal University, Linyi 276005, Shandong, China;
2. College of Mathematics and Physics, Chongqing University, Chongqing 400044, China;
3. Department of Mathematics, Northwest University, Xi’an 710127, Shaanxi,China

Received:2009-11-03 Online:2010-09-16 Published:2010-10-12

摘要/Abstract

摘要：

通过构造一个广义正定径向无界的Lyapunov函数和最优化理论,研究了一个新三维类洛伦兹系统的最终有界集和正向不变集,取得了该系统的三维椭球估计和x-z的二维界估计。然后将得到的变量x,y,z的界应用到混沌同步中,设计了一个尽可能简单的线性控制器,并研究了该系统的完全同步。数值仿真试验证明了同步理论的有效性。

关键词: 最终有界集;正向不变集;混沌同步;数值仿真

Abstract:

The ultimate bound and positively invariant set of a new Lorenz-like system was investigated by constructing a positively definite and radically unbounded Lyapunov function and optimation theory. For this system, the three-dimensional ellipsoidal estimation and two-dimensional estimation about x-z were obtained. Then the upper bound about x,y,z was applied to the chaos synchronization to design a simple linear controller,and its complete synchronization was studied. Numerical simulations were presented to show the effectiveness of the proposed scheme.

Key words: ultimate bound; positively invariant set; chaotic synchronization; numerical simulations

杨洪亮1,张付臣2*,舒永录2,李云超3. 一个新三维类洛伦兹系统的最终有界集和正向不变集及其在同步中的应用[J]. J4, 2010, 45(9): 83-89.

YANG Hong-liang1, ZHANG Fu-chen2*, SHU Yong-lu2, LI Yun-chao3. The ultimate bound and positively invariant set of a new Lorenz-like chaotic system and its application in chaos synchronization[J]. J4, 2010, 45(9): 83-89.

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